A goodness of fit test for mean time to failure function in age replacement

Abstract

Mean time to failure (MTTF) function plays an important role in connection with age replacement policy. In this paper, a goodness of fit test is proposed for MTTF function utilizing a weighted integral as a measure of deviation. The test statistic is shown to be asymptotically normal and the consistency of the test is also established. The proposed test is compared with some parametric tests of exponentiality in the sense of Pitman Asymptotic Relative Efficiency (PARE). The performance of the test is assessed by means of a simulation study. Finally, the test is applied to a real-life data set for illustrative purposes and the results are shown to be in accordance with those obtained by applying the one-sample Kolmogorov-Smirnov test.

Keywords:

• Life distribution
• MTTF function
• asymptotic normality
• Pitman asymptotic relative efficiency
• Monte Carlo simulation

2010 Mathematics Subject Classifications:

• 62G10
• 62N05
• 90B25

Acknowledgements

The authors would like to thank the reviewers and the Editor for their valuable comments and suggestions which have led to a substantial improvement of an earlier version of this paper. The authors are also grateful to the Council of Scientific and Industrial Research (CSIR), India and the University Grants Commission (UGC), India for financial support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors are also grateful to the Council of Scientific and Industrial Research (CSIR), India and the University Grants Commission (UGC), India for financial support.